For point mutations the mutational network is the Hamming graph \(\mathcal {H}(N,2)\)  [1]} (as we can see in Fig REF A, REF B and REF C for \(\mathcal {H}(4,2)\) , \(\mathcal {H}(7,2)\)  and \(\mathcal {H}(10,2)\)  respectively), which is isomorphic to the canonical genotype space \(\mathcal {H}(N,2)=\mathcal {Q}_N\) .
The notion of isomorphism means that the mutational network for point mutations preserves the adjacency of the edge structure of the genotype space.
Historically, the canonical graph of the genotype space overshadowed the richness of the (full) mutation graph, since theoretically only point mutations are usually considered as generators of mutational networks.
For inversions, the mutational network does not necessarily inherit the (local) topology of the genotype space.
For example, Fig REF D, REF E and REF F outline the structure of the mutational networks for inversion mutations for \(N= 4, 7\)  and 10.
From the point of view of graph theory, inversion mutations “rewire” the adjacency of the genotype space, i.e. they link genomes such that \(d_H({\bf x},{\bf x}^{\prime })\ge 1\) .
Also, in graph terms, the total number of accessible mutants per genotype corresponds to the node's degree \(\kappa _{\bf {x}}\)  (defined as the number of edges in the graph incident on \({\bf x}\)  [2]}). Therefore, \(\kappa _{\bf {x}}=D_{\nu }({\bf x})\) .
On the other hand, the average node degree quantifies accessible-mutants (nodes) interconnections:
\(\langle \kappa \rangle :=\frac{1}{2^N}\sum _{{\bf x}} \kappa _{{\bf x}}.\) 
